Quadratic Formula Examples: Roots and Discriminant

The quadratic formula is used when an equation is in the form ax^2 + bx + c = 0. It works even when factoring is difficult, which makes it one of the most dependable algebra tools for students.

The formula

The formula is x = (-b +/- sqrt(b^2 - 4ac)) / (2a). The expression b^2 - 4ac is called the discriminant.

Worked examples

For x^2 - 5x + 6 = 0, a = 1, b = -5, and c = 6. The discriminant is 1, so the roots are 3 and 2.

For x^2 + 4x + 4 = 0, the discriminant is 0, so the equation has one repeated root: x = -2.

Common mistakes

• Forgetting that b can be negative.
• Using 2a only on part of the numerator.
• Not putting the equation into standard form first.

Related tools

Use the Quadratic Formula Calculator for roots, the Algebra Basics Calculator for linear equations, and the Essential Algebra Formulas guide for review.